Modeling complex human behavior, such as voter decisions in national elections, is a long-standing challenge for computational social science. Traditional agent-based models (ABMs) are limited by oversimplified rules, while large-scale statistical models often lack interpretability. We introduce FlockVote, a novel framework that uses Large Language Models (LLMs) to build a "computational laboratory" of LLM agents for political simulation. Each agent is instantiated with a high-fidelity demographic profile and dynamic contextual information (e.g. candidate policies), enabling it to perform nuanced, generative reasoning to simulate a voting decision. We deploy this framework as a testbed on the 2024 U.S. Presidential Election, focusing on seven key swing states. Our simulation's macro-level results successfully replicate the real-world outcome, demonstrating the high fidelity of our "virtual society". The primary contribution is not only the prediction, but also the framework's utility as an interpretable research tool. FlockVote moves beyond black-box outputs, allowing researchers to probe agent-level rationale and analyze the stability and sensitivity of LLM-driven social simulations.